The Thynne family and the Marquis of Bath
According to the Stemmata Botevilleana the Thynne family were formerly known as Botevyle and are descended from the same root. There is no firm proof for this and some sources indicate the contrary.
The story goes that at one time there were so many Botevyles in Church Stretton that they had to have another way in which to distinguish between themselves. One such was Thomas Botevyle who became known as Thomas de la Ynne (or in English Thomas “at the Inn”). This became shortened over time to Thomas Thynne. Hence it is assumed that the name Thynne came into existence.
This is of course the line of the Marquis of Bath so there is a considerable amount of information available to research here, much of which is beyond the scope of this web site.
See the Autobiography of the 7th Marquis of Bath.
For more about the Thynne claims of decent from Sir Geoffrey de Botevyle see Thynne, Viscount Weymouth. See also references here from Debretts where the name changed from Botevyle to Thynne.